Many in line P25174

Write a program that reads cubes n × n × n of integer numbers and computes how many lines of size m contains, for any m between 2 and n. Here, a line is a sequence of identical integer numbers adjacents in the same direction. The considered directions are vertical, horizontal, of depth, (in total, 26 senses, in 13 directions).

Input

Input consists of a sequence of cube descriptions separated by an empty line. Each description starts with a natural n ≥ 2. n descriptions of each plane of the cube follow, separated by an empty line, each plane has n rows with n integer numbers each one.

Output

for each cube, print how many lines of size m contains, for any m between 2 and n. Follow the format of the examples. Separate the different outputs with an empty line.